Search: id:A002320
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%I A002320
%S A002320 1,3,14,67,321,1538,7369,35307,169166,810523,3883449,18606722,
%T A002320 89150161,427144083,2046570254,9805707187,46981965681,225104121218,
%U A002320 1078538640409,5167589080827,24759406763726,118629444737803
%N A002320 a(n) = 5*a(n-1) - a(n-2).
%C A002320 Together with A002310 these are the two sequences satisfying ( a(n)^2+a(n-1)^2 
               )/(1 - a(n)a(n-1)) is an integer, in both cases this integer is -5. 
               - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 26 2001
%D A002320 From a posting to Netnews group sci.math by ksbrown(AT)seanet.com (K. 
               S. Brown) on Aug 15 1996.
%H A002320 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A002320 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A002320 MathPages, <a href="http://www.mathpages.com/home/kmath334.htm">N = (x^2 
               + y^2)/(1+xy) is a Square</a>
%F A002320 Sequences A002310, A002320 and A049685 have this in common: each one 
               satisfies a(n+1) = (a(n)^2+5)/a(n-1) - Graeme McRae (g_m(AT)mcraefamily.com), 
               Jan 30 2005
%F A002320 G.f.: (1-2x)/(1-5x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 16 2008]
%F A002320 a(n)=-(1/42)*sqrt(21)*[(5/2)-(1/2)*sqrt(21)]^n+(1/42)*[(5/2)+(1/2)*sqrt(21)]^n*sqrt(21)+(1/
               2)*[(5/2) +(1/2)*sqrt(21)]^n+(1/2)*[(5/2)-(1/2)*sqrt(21)]^n, with 
               n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 21 2008]
%Y A002320 Sequence in context: A026592 A034275 A151322 this_sequence A151323 A113140 
               A151324
%Y A002320 Adjacent sequences: A002317 A002318 A002319 this_sequence A002321 A002322 
               A002323
%K A002320 nonn
%O A002320 0,2
%A A002320 Joe Keane (jgk(AT)jgk.org)

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